Question: In the equation, $\frac15+\frac{5}{x}=\frac{12}{x}+\frac{1}{12}$, what is the value of $x$?
Subtract $\frac{5}{x}$ and $\frac{1}{12}$ from both sides of the equation to obtain \[
\frac{7}{60}=\frac{7}{x}.
\] By inspection, the solution of this equation is $x=\boxed{60}$.